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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 1, Pages 211–224 (Mi izv1237)  

This article is cited in 4 scientific papers (total in 4 papers)

The distribution of Hardy–Littlewood numbers in arithmetic progressions

Z. Kh. Rakhmonov


Abstract: An asymptotic formula is obtained for the number of solutions of the congruence
$$ p+n^2\equiv l (\operatorname{mod}D),\qquad p\leqslant x,\quad n\leqslant\sqrt x,\quad(l,D)=1, $$
where $D$ is a sufficiently large prime.
Bibliography: 7 titles.

Full text: PDF file (983 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:1, 213–228

Bibliographic databases:

UDC: 511
MSC: 11N64, 11N37
Received: 15.06.1987

Citation: Z. Kh. Rakhmonov, “The distribution of Hardy–Littlewood numbers in arithmetic progressions”, Izv. Akad. Nauk SSSR Ser. Mat., 53:1 (1989), 211–224; Math. USSR-Izv., 34:1 (1990), 213–228

Citation in format AMSBIB
\Bibitem{Rak89}
\by Z.~Kh.~Rakhmonov
\paper The distribution of Hardy--Littlewood numbers in arithmetic progressions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 1
\pages 211--224
\mathnet{http://mi.mathnet.ru/izv1237}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=992985}
\zmath{https://zbmath.org/?q=an:0692.10037|0671.10042}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 213--228
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000621}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Z. Kh. Rakhmonov, “Theorem on the mean value of $\psi(x,\chi)$ and its applications”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 49–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Z. Kh. Rakhmonov, “A theorem on the mean value of Chebishev functions”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 555–569  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Rakhmonov Z., “Mean Value Theorems in Prime Number Theory”, Dokl. Akad. Nauk, 349:5 (1996), 606–607  mathnet  mathscinet  zmath  isi
    4. A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters”, Russian Math. Surveys, 63:4 (2008), 641–690  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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